The Nonlinear Lopsided HSS-Like Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems with Positive-Definite Matrices

doi:10.1007/s42967-019-00038-5

Communications on Applied Mathematics and Computation ›› 2021, Vol. 3 ›› Issue (1): 109-122.doi: 10.1007/s42967-019-00038-5

• ORIGINAL PAPER • 上一篇下一篇

The Nonlinear Lopsided HSS-Like Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems with Positive-Definite Matrices

Lu Jia¹, Xiang Wang^1,2, Xiao-Yong Xiao¹

1 Department of Mathematics, Nanchang University, Nanchang 330031, China;
2 Numerical Simulation and High-Performance Computing Laboratory, Nanchang University, Nanchang 330031, China

收稿日期:2019-03-01 修回日期:2019-07-06 出版日期:2021-03-20 发布日期:2021-03-15
通讯作者: Xiang Wang, wangxiang49@ncu.edu.cn E-mail:wangxiang49@ncu.edu.cn
基金资助:
This work is supported by the National Natural Science Foundation of China with No. 11461046, the Natural Science Foundation of Jiangxi Province of China with Nos. 20181ACB20001 and 20161ACB21005.

The Nonlinear Lopsided HSS-Like Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems with Positive-Definite Matrices

Lu Jia¹, Xiang Wang^1,2,Xiao-Yong Xiao¹

1 Department of Mathematics, Nanchang University, Nanchang 330031, China;
2 Numerical Simulation and High-Performance Computing Laboratory, Nanchang University, Nanchang 330031, China

Received:2019-03-01 Revised:2019-07-06 Online:2021-03-20 Published:2021-03-15
Contact: Xiang Wang, wangxiang49@ncu.edu.cn E-mail:wangxiang49@ncu.edu.cn
Supported by:
This work is supported by the National Natural Science Foundation of China with No. 11461046, the Natural Science Foundation of Jiangxi Province of China with Nos. 20181ACB20001 and 20161ACB21005.

摘要/Abstract

摘要： In this paper, by means of constructing the linear complementarity problems into the corresponding absolute value equation, we raise an iteration method, called as the nonlinear lopsided HSS-like modulus-based matrix splitting iteration method, for solving the linear complementarity problems whose coefficient matrix in R^n×n is large sparse and positive definite. From the convergence analysis, it is appreciable to see that the proposed method will converge to its accurate solution under appropriate conditions. Numerical examples demonstrate that the presented method precede to other methods in practical implementation.

关键词: Linear complementarity problem, Modulus-based matrix splitting, Lopsided HSS

Abstract: In this paper, by means of constructing the linear complementarity problems into the corresponding absolute value equation, we raise an iteration method, called as the nonlinear lopsided HSS-like modulus-based matrix splitting iteration method, for solving the linear complementarity problems whose coefficient matrix in R^n×n is large sparse and positive definite. From the convergence analysis, it is appreciable to see that the proposed method will converge to its accurate solution under appropriate conditions. Numerical examples demonstrate that the presented method precede to other methods in practical implementation.

Key words: Linear complementarity problem, Modulus-based matrix splitting, Lopsided HSS

中图分类号:

65F30
65F50

Lu Jia, Xiang Wang, Xiao-Yong Xiao. The Nonlinear Lopsided HSS-Like Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems with Positive-Definite Matrices[J]. Communications on Applied Mathematics and Computation, 2021, 3(1): 109-122.

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The Nonlinear Lopsided HSS-Like Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems with Positive-Definite Matrices

The Nonlinear Lopsided HSS-Like Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems with Positive-Definite Matrices

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